On GCT-Invariant Operator Ordering Rule

With an observation that the general coordinate transformation (GCT) invariant operator ordering rule proposed by DeWitt is valid only for some cases, a careful classification for classical observables that can be related through the well-defined GCT is presented and a generalized GCT-invariant ordering rule is derived.     

Hidden Symmetries in the Two-Dimensional Isotropic Antiferromagnet

We discuss the two-dimensional isotropic antiferromagnet in the framework of gauge invariance. Gauge invariance is one of the most subtle useful concepts in theoretical physics, since it allows one to describe the time evolution of complex physical system in arbitrary sequences of reference frames. All theories of the fundamental interactions rely on gauge invariance. In Dirac’s approach, the two-dimensional isotropic antiferromagnet is subject to second-class constraints, which are independent of the Hamiltonian symmetries and can be used to eliminate certain canonical variables from the theory. We have used the symplectic embedding formalism developed by a few of us to make the system under study gauge invariant. After carrying out the embedding and Dirac analysis, we systematically show how second-class constraints can generate hidden symmetries. We obtain the invariant second-order Lagrangian and the gauge-invariant model Hamiltonian. Finally, for a particular choice of factor ordering, we derive the functional Schröodinger equations for the original Hamiltonian and for the first-class Hamiltonian and show them to be identical, which justifies our choice of factor ordering.     

Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions

We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In the process, we define the appropriate generalization of some key QFT notions, including connectedness, locality and contraction of (high) subgraphs. We also define a new notion of Wick ordering, corresponding to the subtraction of (maximal) melonic tadpoles. We then consider the simplest examples of dynamical 4-dimensional TGFT with gauge invariance conditions for the Abelian U(1) case. We prove that they are super-renormalizable for any polynomial interaction.     

Corrections to angular ordering in multiple hadroproduction

One of the key ideas in describing the multiparticle production at high energies in the perturbative QCD is the angular ordering in successive soft-gluon emission. We analyse the angular distribution of particles in a jet, and investigate the corrections to the angular ordering. At a small angle from the jet direction, the angular ordering is exact at the next-to-leading order. At a large angle, the angular ordering overestimates the angular particle density by a factor (1?γln cos²(γ/2)), whereγ is the anomalous dimension of the multiplicity. TheO(γ) correction restores the boost invariance of the cross section.     

Quantum spinning particle in a curved metric

We show that the combined use of N=1 supersymmetry and general coordinate invariance allows to completely fix the operator ordering ambiguity for a non-relativistic interacting spinning particle.     

Photon-Number Distribution and Wigner Function of Generalized Squeezed Thermal State

In this paper, we present the density operator of the generalized squeezed thermal state (GSTS) and obtain its normal ordering form by virtue of the technique of integration within an ordered product of operators and the Weyl ordering invariance under similarity transformations. Some significant quantum statistical properties of the GSTS are investigated, such as the photon-number distribution (PND) and the Wigner function (WF). It is found that the PND of the GSTS is a Legendre polynomial, and its squeezed vacuum oscillations imply the nonclassicality, as well as the GSTS whose WF has no negative region is indeed a special type of nonclassical state.     

Constraint algebra for interacting quantum systems

We consider relativistic constrained systems interacting with external fields. We provide physical arguments to support the idea that the quantum constraint algebra should be the same as in the free quantum case. For systems with ordering ambiguities this principle is essential to obtain a unique quantization. This is shown explicitly in the case of a relativistic spinning particle, where our assumption about the constraint algebra plus invariance under general coordinate transformations leads to a unique S-matrix.     

单双模连续压缩真空态及其量子统计性质

利用有序算符内的积分技术研究了通过双模压缩算符作用于两个单模压缩 态上得到的单双模 连续压缩态. 导出了单双模连续压缩算 符的正规乘积形式, 并在此基础上研究了单双模连续压缩真空态的量子统计性质. 特别是利用Weyl编 序算符在相似变换 下的不变性, 简洁地导出了单双模连续 压缩真空态的Wigner函数. 最后, 还简单地提出 了单双模连续压缩 真空态的实验产生方案.     

广义压缩粒子数态的非经典性质及其退相干

研究了三参数的压缩算符产生的广义压缩粒子数态的非经典性质及其在光子损失通道中的退相干问题.利用有序算符内的积分技术和Weyl编序算符在相似变换下的不变性,简洁地导出了广义压缩粒子数态的Wigner函数(Laguerre-Gaussian函数).基于Wigner函数的演化积分公式,解析地推导出了在耗散通道中的Wigner函数表达式.特别地,根据Wigner函数负部体积讨论了其非经典性.     

Tuning the effects of Landau level mixing on anisotropic transport in quantum Hall systems

Electron-electron interactions in half-filled high Landau levels in two-dimensional electron gases in a strong perpendicular magnetic field can lead to states with anisotropic longitudinal resistance. This longitudinal resistance is generally believed to arise from broken rotational invariance, which is indicated by charge density wave order in Hartree-Fock calculations. We use the Hartree-Fock approximation to study the influence of externally tuned Landau level mixing on the formation of interaction-induced states that break rotational invariance in two-dimensional electron and hole systems. We focus on the situation when there are two non-interacting states in the vicinity of the Fermi level and construct a Landau theory to study coupled charge density wave order that can occur as interactions are tuned and the filling or mixing are varied. We consider numerically a specific example where mixing is tuned externally through Rashba spin-orbit coupling. We calculate the phase diagram and find the possibility of ordering involving coupled striped or triangular charge density waves in the two levels. Our results may be relevant to recent transport experiments on quantum Hall nematics in which Landau level mixing plays an important role.     

Two-step magnetic ordering in quasi-one-dimensional helimagnets: possible experimental validation of villain's conjecture about a chiral spin liquid phase

Low-temperature specific heat, magnetic susceptibility, and zero-field muon spin resonance (microSR) measurements have been performed in the quasi-one-dimensional molecular helimagnetic compound Gd(hfac)3NITEt. The specific heat presents two anomalies at T(0)=2.19+/-0.02 K and T(N)=1.88+/-0.02 K, which both disappear upon the application of a weak magnetic field. Conversely, magnetic susceptibility and muSR data show the divergence of two-spin correlation functions only at T(N)=1.88+/-0.02 K. These results suggest an experimental validation of Villain's conjecture of a two-step magnetic ordering in quasi-one-dimensional XY helimagnets; i.e., the paramagnetic phase and the helical spin solid phase are separated by a chiral spin liquid phase, where translational invariance is broken without violation of rotational invariance.     

Star-products and phase space realizations of quantum groups

It is shown for a family of *-products (i.e. different ordering rules) that, under a strong invariance condition, the functions of the quadratic preferred observables (which generate the Cartan subalgebra in phase space realization of Lie algebras) take only the linear or exponential form. An exception occurs for the case of a symmetric ordering *-product where trigonometric functions and two special polynomials can also be included. As an example, the quantized algebra of the oscillator Lie algebra is argued.     

Physics of a Kind of Normally Ordered Gaussian Operators in Quantum Optics

Based on the technique of integration within an ordered product of operators we investigate a completeness relation of pure states （such as the coordinate eigenstate, the momentum eigenstate and the coherent state） into normally ordered Gaussian forms. The Weyl ordering invariance under similarity transformations is employed to reveal physical meaning of a kind of normally ordered Gaussian operators, which have the similar forms to the bivariate normal distributions in statistics, i.e., the thermo mixed state density matrix.     

Squeezing Properties of the Generalized Multimode Squeezed States

By means of the invariance of Weyl ordering under similar transformations we derive the explicit form of the generalized multimode squeezed states.Moreover,the completeness relation and the squeezing properties of the generalized multimode squeezed states are discussed.     

Entanglement Rule of Wigner Operators at a Beamsplitter

It is known that beamsplitter can be used to produce quantum entanglement, in this paper we examine this topic from the point of view of Wigner operators. Using Weyl-ordering of the Wigner operator and the Weyl ordering invariance of Weyl ordered operators under similarity transformation we derive the entanglement rule of Wigner operators at a beamsplitter.     

On the Radon transformation of Wigner function altered with various optical processes

We discuss what happens to the Radon transformation of signal's Wigner functions (i.e., signal's Wigner transformation (WT)) if the signal function undergoes various optical processes, such as Fraunhofer diffraction, lens transformation and Fresnel diffraction, etc. Because the usual Wigner transforms can be studied via their corresponding transforms of the Wigner operator, we use the Weyl ordered form of the Wigner operator and the Weyl ordering invariance under similar transformations to derive the result, we find that the alteration of Radon transformation of signal's Wigner function (or named the variation of tomogram function), through these optical processes, can be ascribed to the variation of Radon transformation parameters once the parameter of WT is given.     

The relationship between the conformal and gravitational anomalies

It is shown that the vectorial part of the general coordinate transformation (GCT) anomaly cannot be eliminated by local counterterms without generating the conformal anomaly for the system with classical GCT and conformal symmetries. The vectorial part of the GCT anomaly is equivalent to the non-topological conformal anomaly similarly as the chiral part of the GCT anomaly is equivalent to the topological Lorentz anomaly. In two dimensions, the conformal anomaly is topological, and equivalent to the Lorentz anomaly up to the factor i for the left (or right) part contribution only.     

Quantized equations of motion in non-commutative theories

Quantum field theories based on interactions which contain the Moyal star product suffer, in the general case when time does not commute with space, from several diseases: quantum equation of motions contain unusual terms, conserved currents cannot be defined and the residual spacetime symmetry is not maintained. All these problems have the same origin: time ordering does not commute with taking the star product. Here we show that these difficulties can be circumvented by a new definition of time ordering: namely with respect to a light-cone variable. In particular the original spacetime symmetries and translation invariance turn out to be respected. Unitarity is guaranteed as well.Received: 12 January 2005, Revised: 16 March 2005, Published online: 18 May 2005